The way to distinguish between random radar signals

 

(57) Abstract:

The invention relates to methods for increasing the noise immunity of the data transmission line. The technical result is to increase the probability of distinguishing two random pulse signals having different average power. How is that radar signals reflected from objects locations, detects, from the output of the detector signals branch into two channels and simultaneously fed to the inputs of the two channels of processing the values of the amplitudes of videokursov. In one channel values of the amplitudes of videokursov square, summarize, determine a threshold value, compare the sum of the values of the amplitude with a threshold value. In the other channel values of the amplitudes of videokursov erected in the degree a lot more than the second, the converted values of the amplitudes summarize, determine a threshold value, compare the sum of the values of the amplitude with a threshold value of the second channel. Decide, which of the two signals passed signal with a higher average power, if at least one of the channels, the sum of the converted values of the amplitudes exceed the threshold level of that channel. 8 Il., 7 table.

The invention relates to a method of the channels, transmitted on these lines, to one or another class of signals. The invention can be used in radar systems to detect signals on the background noise and object recognition locations, as well as in other fields where it is necessary to carry out the classification of aggregates (threads) random variables.

Known way to distinguish between random signals [1, page 215, 221, 242], based on the measurement for a certain period of time the values of the amplitudes of videokursov random signals and calculating the likelihood ratio:

(x) =2(x)/1(x) (1)

or any monotonic function of this ratio, for example

l(x) = ln(x), (2)

where1(x)2(x) is known a priori differential distribution of values of amplitudes of videokursov distinguish between two random signals; l(x) - natural logarithm of the likelihood ratio.

If the signals represented by the sample of N values of the amplitudes of videokursov, the natural logarithm of the likelihood ratio has the form [1, page 221]:

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To distinguish the signals necessary to determine the threshold value l(x), which we denote l0. If l(x) exceeds the value of l0then consider that passed the signal from the door0is calculated on the basis of one criterion, which is a special case of the criterion likelihood ratio criterion weighted combination, the criterion of the ideal observer, the criterion of Neyman-Pearson criterion sequential observer. The order of calculation according to these criteria is given in [1, pages 216-223].

From the formula (3) shows that the process of discernment is reduced to the following operations: amplitude value of the pulse signal is subjected to conversion

f(x) = ln[2(x)/1(x)], (4)

the converted values of the amplitudes of the sum and the sum of these amplitudes is compared with a threshold value of l0.

Also known way to distinguish between random signals used in radar systems [2, pages 124 and 3, page 355, 366], and selected as a prototype of the invention. It is known [1, page 113] that the values of the amplitudes of videokursov radar signals and noise at the output of the receiver detector radar measured for a certain period of time (long enough properties of the sample could be transferred to the General population) random and distributed according to the following laws [1, page 113]: if the input of the detector applies a random signal with a normal distribution of mcneven ctor described by Rayleigh:

(x) = (2x/p)exp(-x2/p), (5)

where p is the parameter of the distribution, equal to the second initial moment (from the physical point of view - the average power of the signal); if the input of the detector operates, the amount of noise and random signal with amplitude a, then the distribution of values of the amplitudes of videokursov total signal at the output of the detector is represented by the law rice (generalized Rayleigh distribution):

(x) = (2x/p)exp[-(x2+a2)/p]I0(xa/p), (6)

where l0(xa/p) is the Bessel function of zero order from the imaginary argument.

On page 366 [3] shows that for distinguishing signals having the distribution (5), it is necessary to sum the squares of the values of the amplitudes of videokursov and compare the sum with a threshold. To distinguish between signals with the distribution (6) to sum values of the amplitudes of videokursov converted by the formula

f(x)=lnI0(xa/p), (7)

Prototype method consists in the following. Serves radar signals reflected from objects location, to the input of the detector at time t, with the detector output signal on one channel processing of the values of the amplitudes of videokursov, where they were functional transformation f(x) and the sum of the N values of the transformed amplitudes videomonitor Yoand compare the sum of the values of the amplitudes of videokursov Y with the threshold value of Yo.

For small signal to noise ratio (CA/p<<l) lnI0(ha/p) and for large relations (ha/p>>l) lnI0(xa/p) dx, where d is a constant [2, page 125]. Therefore, in all cases in the prototype case, the procedure of discernment is reduced to the summation of the values of the amplitudes of videokursov or their squares and comparing the sum with a given threshold. It is obvious that to solve the problem of distinguishing the most interesting case of small relations capacities of signal and noise. Therefore, in the invention as a prototype of the selected procedure of discernment, which consists in summing the squares of the values of the amplitudes of videokursov, i.e. f(x) = x2and comparing the sum with a given threshold.

To assess the quality of discernment in the prototype used a procedure derived from the criterion of Neyman-Pearson [1, page 220].

Using the procedure there are two signals with different average capacity and, consequently, with different average values of the amplitudes of videokursov. The procedure of distinguishing signals described below. In this case the sum of the values of the amplitudes of videokursov denote by the symbol Y and the threshold value of Y0.

1. Vicie, corresponding to the signal with a lower average power, P2(Y) - more. The definition of the integral of the distributions given in [6, page 43]. To calculate the P1(Y) and P2(Y) use one of the well-known in probability theory methods, such as the Central limit theorem or method of characteristic functions [6, page 135, 149].

2. Set the probability of F threshold Y0sums of values of amplitudes of the signal with a lower average power.

3. Calculate the threshold value of the sums of Yoby solving the equation:

F=P1(Y0), (8)

relative values of Y0.

4. Calculates the probability of D threshold amounts amplitudes videokursov signal with a higher average power:

D=P2(Y0) (9)

The quality of discernment is higher, the greater the probability of D for a given probability f

Similar and prototype have drawbacks. With a small difference between the parameters distinguish signals (for example, between the average capacity) and a small number of values summed amplitudes videokursov the probability of discernment will be low. In addition to the exact job of the signal processing necessary a priori know the law bespredel increase the probability of distinguishing two random pulse signals, having different average power.

This result is achieved due to the fact that the way to distinguish between random radar signals is that radar signals reflected from objects locations, serves on the input of the amplitude detector at time t and detects them. At the detector output signals branch into two channels. The branched signals are simultaneously fed to the inputs of the two channels of the processing of the amplitudes of videokursov. The values of the amplitudes of videokursov in one processing channel square, then the sum of the N values of the transformed amplitudes videokursov, and N = t/T where T is the repetition period of videokursov determine the threshold value of the sum of the values of the amplitudes of Yo,1then compare the sum of the converted values of the amplitudes of videokursov Y1with a threshold value of Yo,1. In the second processing channel values of the amplitudes of videokursov erected in the degree a lot more than the second, it is assumed degree a lot more than the second, if it is five times or more than the second degree. The converted values of the amplitudes in the first and second channels summarize, determine the threshold values of these sums Yo,1and Yo 2each sum value and Yo 2your channel. Decide, which of the two signals passed signal with a higher average power, if at least one of the channels, the sum of the converted values of the amplitudes of Y1or Y2will exceed the level of Yo,1or Yo 2the threshold of her channel.

Distinctive features of the invention are: simultaneous branching of the signal at the detector output into two channels; applying to the inputs of the first and second channel processing amplitudes videokursov branched signal; exponentiation lot more second values of the amplitudes of videokursov in the second processing channel; the sum of the converted values of the amplitudes in the second processing channel; determining a threshold amount of the converted values of the amplitudes in the second processing channel Yo 2; comparing the sum of the values of the transformed amplitudes Y2the second channel with a threshold value of Yo 2this channel; the decision about which of the two signals passed signal with a higher average power, if at least one of the channels, the sum of the converted values of the amplitudes of Y1or Y2will exceed the level of Yo,1or Yo,1the threshold of her channel.

The proposed method according to the scheme of arrangement, which can be implemented in a way which has been introduced notations: 1 - peak detector receiver radar; 2 - splitter signal into two channels; 3 - device for raising the values of the amplitudes of videokursov square; 4 - a device for raising the values of the amplitudes of videokursov in degree n many more second; 5 - adder converted values of the amplitudes of the first channel; 6 - adder converted values of the amplitudes of the second channel; 7 - threshold device of the first channel; 8 - threshold device of the second channel; 9 - device decision-making.

To implement this device (Fig. 1) in the following way. The values of the amplitudes of videokursov using analog-to-digital Converter converts the digital code, and then simultaneously fed to the inputs of two parallel processors. In the processor of the first channel values of the amplitudes of the square. In the processor of the second channel values of the amplitudes are given a degree n many more than the second.

In the processors of the two channels summarize the converted values of the amplitudes of the signals and their sum is compared with the threshold.

In Fig. 2 shows the dependence of the probability of distinguishing two radiolog the Oia (k values) of the distribution of values of amplitudes (calculation, the Rayleigh distribution, N = 50000).

In Fig. 3 shows the dependence of the probability of distinguishing two radar signals and the exponent n (n=1 to 1000) transformed amplitudes at different degrees of restrictions (values of k) distribution of values of amplitudes (experiment, the Rayleigh distribution, N = 50000).

In Fig. 4 shows the dependence of the probability of distinguishing two radar signals and the exponent n (n=1 to 1000) transformed amplitudes at different degrees of restrictions (values of k) distribution of values of amplitudes (experiment, the Rayleigh distribution, N =10).

In Fig. 5 shows the dependence of the probability of distinguishing two radar signals and the exponent n (n=1 to 1000) transformed amplitudes at different degrees of restrictions (values of k) distribution of values of amplitudes (calculation, distribution Thinning and rice, N = 50000).

In Fig. 6 shows the dependence of the probability of distinguishing two radar signals and the exponent n (n=1 to 1000) transformed amplitudes at different degrees of restrictions (values of k) distribution of values of amplitudes (calculation, gamma distribution, N = 50000).

In Fig. 7 shows the dependence of the probability difference is but limited amplitudes (calculation and experiment, signals with different levels of restrictions, N = 50000).

In Fig. 8 shows the dependence of the probability of distinguishing artificially limited random signal and sums this signal with a non-random signal and the exponent n (n = 1 -1000) (calculation and experiment, N = 50000).

An example implementation of the method of distinguishing a random radar signals.

To the input of detector 1 (Fig. 1) at time t the signals reflected from objects, locations, and detects them. These signals from the output of the detector using a splitter 2 is divided into two channels and simultaneously serves two channel processing of the N values of the amplitudes of videokursov (N = t/T where T is the repetition period of videokursov). In the first channel containing device 3 of the transition amplitudes, the adder 5 converted amplitude and the threshold device 7, the values of the amplitudes of videokursov you square in the conversion device 3. The converted values of the amplitudes of the sum in the adder 5 and the sum of Y1compared with the threshold value of Yo,1in the threshold device 7. In the second channel containing device 4 conversion, the adder 6 converted amplitudes and threshold device 8, the values of the amplitudes of videokursov erected in grade is D. summed in the adder 6 and the sum of Y2compared with the threshold value of Yo 2in the threshold device 8.

To determine threshold values of Yo,1and Yo 2set the probability of F exceeding the threshold amounts Y1and Y2corresponding to the signal with a lower average power, and the value of F is set for both channels the same. Then determine the cumulative distribution of the amounts specified above signal in the first P1(Y1and in the second P1(Y2) channels. Finally, to calculate the values of Yo,1and Yo 2solve the equation

F=P1(Yo,1), F=P1(Yo 2), (10)

relative values of Yo,1and Yo 2.

Cumulative distribution of P1(Y1) and P1(Y2) is calculated using the known methods of probability theory, for example, the method of characteristic functions, or by using the Central limit theorem of probability theory [6, page 135, 149] (see the description of the prototype). Compare the amount converted amplitudes Y1and Y2threshold values of Yo,1and Yo 2your channel with threshold devices 7 and 8 (Fig. 1).

If at least one of the channels, the sum of the converted amplitude Y1or Y2amplitudes pre signals passed signal with a higher average power.

Show a causal link characteristics of the invention with achievable technical result - increasing the likelihood of distinguishing random signals. For a start, pay attention to the following important circumstance.

Distribution of values of the amplitudes of the real signals are theoretical laws (Rayleigh, rice, student, and others), which are used for the development of procedures for processing signals in their discernment. But this view cannot be regarded as fully justified, because these laws, albeit with low probability, but allow the emergence of large amplitudes, including tending to infinity. In real conditions the appearance of signals with infinitely large values of the amplitudes is excluded. The appearance just large amplitudes, many times exceeding the average value, it is unlikely. This means that when observing real tones you can get a large sample of values of amplitudes that are restricted to the top end level. Under the expression "large samples" you see samples with the same number of values of the amplitudes, which is sufficient for effective differentiation signals.

Note that the real stochniol

x (z)=A[I-exp(-gz2)], (11)

where x and z - amplitude of the output signal and the input device; A and g are constants.

From (11) we see that for any value of z, the amplitude x at the output of the device cannot be greater than the value of A. This also argues in favor of approval on the limitation of real amplitudes of the signals.

We show that the limited values of the amplitudes allows to obtain more effective differentiation of signals than give ways similar and prototype. To assess the probability of distinguishing apply the criterion of Neyman-Pearson, which is a special case of the criterion likelihood ratio [1, page 220]. This criterion is used in the prototype. Using the criterion to distinguish between two signals with different average capacity and, consequently, with different average amplitudes. The procedure of discernment in accordance with this criterion is the following. Set the probability of F exceeding some threshold amplitude signal with a lower average power. Then, on the basis of information on the statistical parameters of the signal and a given probability F determine the threshold value. Finally, compute the probability of D exceeding a threshold amplitude of another signal having a higher middle. the quality of discernment is higher, the greater the likelihood of D given f

Suppose that the amplitude of the random signal x lie within a limited range 0xx0and within these limits, their differential distribution is well described by the law of (x) allowing the emergence of values of x tending to infinity. Then the distribution of values of the amplitudes of the considered signal is equal to k (x), where the coefficient k is determined from the equation

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The coefficient k1 and the more, the less x0, i.e. the higher the degree of limited amplitude. Thus, this coefficient characterizes the degree of limitation of the real distribution of amplitudes compared to those that allow theoretical distribution.

Let the procedure distinction is that the amplitude of x is transformed according to the formula

y=xn, n1, (13)

and then added together and the sum is compared with a threshold. Determine the dependence of the quality of discernment on the degree of limited amplitude, i.e. the value k, and the exponent n in (13).

To use the criterion of Neyman-Pearson, you must define the laws of distribution amounts. However, we note that because the value of x lies within 0. . . x0then x2">

Let the value of N is large enough. Then on the basis of the Central limit theorem of probability theory we assume that the distribution of the amounts described normal law 16, page 150, 154]. In this case, the differential distribution amounts will be

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where Y is the sum of N random variables y; m is the expectation value y;2the variance of the values of y; L - coefficient taking into account that the sum of Y lies in the range 0... N(x0)n.

The factor L is determined from the equation

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Using the formula to calculate the probability of a random variable, distributed according to the normal law, for a specified time interval 0... N(x0)n[4, page 116], get:

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where is the integral of probabilities.

The value of L may be an indirect sign of justified use of the Central limit theorem: the closer L to unity, the closer the distribution of (14) to the canonical normal.

The probability of exceeding the sum of Y given value (threshold) Y0equal to [4, page 116]

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where

Size m and is calculated as [6, page 118, 78]

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Derive a formula for calculating the probability of correct discernment D when given verojatno elshimi distribution of k11(x) with parameters x01, m11and L1,

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Then

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From the formula (21) shows that if the parameters of the distribution of amplitudes of the first signal and the values of N and F, the argument of the integral of the probability in the left part of equality (21) will have a size equal to

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Where

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To determine the probability of correct discernment of signal 2, with the distribution of the amplitudes of the k22(x), it is necessary to substitute in the formula (17) x02, m2,2and L2and the value of y0. After transformation will receive

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The quality of discernment signals defined in two ways: by calculating the probability of discernment by the above method; by the experimental determination of the probability of discernment using as the amplitudes of the random numbers distributed according to given laws.

The second method used to test the first and to determine the probability of distinguishing signals with a small number of summed amplitudes, when you cannot use the Central limit theorem to calculate the values of F and d

In the first method, the calculation of the quantities m , L, and D performed by the numerical method in the early relatively large (N = 50000). For the same reason, was considered reliable only those results in which the ratio of L does not exceed the value of 1.01. This procedure to differentiate between the two signals, labeled 1 and 2. The threshold y0configured such that the first signal having a smaller average power exceeded its fixed probability F. the Probability of exceeding the threshold of the second signal calculated by the formula (24).

The second method to simulate the signal amplitude used random numbers generated by computer and having a set of differential distribution. Given the degree of restriction of distributions obtained by dropping numbers greater than a certain value. The number raised to the power n and summed over N pieces. Defined threshold amounts that exceed the amounts that simulates the first signal, with a probability of F. Then determines the probability of exceeding threshold amounts, simulating the second signal (the value of D ).

The results of calculations and experiments are presented in tables 1 -7 and graphs Fig. 2 - 8, which lists the values of D as a function of the exponent n and k-factor. The dashes in the tables correspond to the values n and k, where L > 1, that is, the Nar is when the exponent n = 2 the procedure of distinguishing signals corresponds to the prototype of the invention.

In table 1 and the graphs of Fig. 2 presents the results of the calculation differentiate between the two signals, the amplitude of which is distributed within 0xx0according to Rayleigh (5) and have the parameters k1p1and k2p2. Conditions of relative boundedness of the amplitudes of both signals are set to the same, so k1= k2= k. The ratio of average signal power is set to p2/ p1= 1.01, the probability of exceeding a threshold signal with a lower average power is set equal to F = 0,001. When F = 0,001 value C = 1,19 [4, page 551].

In table 2 and the graphs of Fig. 3 presents the results of experimental verification of the result made by the second method of assessing the quality of discernment. Here also the number of summed values of y equal to 50000, and the number of sums in each signal that is defined threshold F and D, is set equal to 10000. A large number of amounts selected to obtain reliable results.

Given the rate limiting distributions obtained in the following way. Substituting the Rayleigh distribution in equation (12), and solving the equation for values of x0get

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Distribution with the specified constraint obtained by discarding when Iceni more signals than that of the prototype (n = 2), and increases with increasing n.

Assessment of the quality of discernment with a small number of summed values of the amplitudes of the performed experiment. In table 3 and Fig. 4 presents the results for signals with Rayleigh distribution amplitudes for N = 10, p2/p1= 3 and F = 10-5.

From table. 3 and Fig. 4 shows that when n = 10 (n >2) and k >1, the probability of distinguishing signals greater than that of the prototype (n = 2).

Analysis of the results of tables 1 to 3 allows us to draw the following conclusions:

1. Signals with a limited distribution amplitudes (k >1) it is possible to distinguish more effectively than it allows to do a prototype. For this purpose it is necessary to sum values of the amplitudes, raised to the power of n >2. So, for example, tables 1 and 2 show that the prototype (n = 2) to obtain D = 0.16.. . 0.25. Under these same conditions, the method according to the invention gives for n = 1000 D = 0.78... 1.0.

2. The method according to the invention is most effective in the most difficult cases, when small difference between the parameters distinguish signals: here is the difference in effectiveness between invention and prototype the most significant. This can be seen when comparing the results in tables 1 and 2, where p2/p1= 1.01, table 3 (p2/p01 the results of the experiment are shown in table 2, give: if n = 2D = 0.23, n = 200 D = 0.999.

In table. 4 and Fig. 5 presents the results of the calculation of the probability of distinguishing the first signal having values of amplitudes with a Rayleigh distribution (5) and second signals representing the amount of noise and random signal with the amplitude and distribution of rice (6)). The case is a typical case detection signal against the background noise. In the calculations is set to p = 0.1; a = 0.03; F = 10-6.

From table. 4 and Fig. 5 shows that when n = 100 (n >>2) and k >1, the probability of distinguishing signals greater than that of the prototype (n = 2), and increases with increasing n.

In table. 5 and in Fig. 6 presents the results distinguish between signals, the values of amplitudes which have a gamma distribution [5, page 56]. In the calculations set to p2/p2= 1.01 and F = 0,001.

From table. 5 and Fig. 6 shows that when n = 20 (n>>2) and k >1, the probability of distinguishing signals greater than that of the prototype (n = 2), and also increases with increasing n.

Of particular interest is the case where the amplitude limitation is the result of passing the signal through a device with limited dynamic range. Typical amplitude characteristic of such devices is described by the formula (11).

the STV with amplitude characteristic (11), moreover, the signals pass through different devices, different parameter And amplitude characteristics. Z-values of the amplitudes of the signals are random and are at the inputs of the devices have the same distribution w(z). The maximum values of the amplitudes at the outputs of the devices is equal to A1and A2and A1< A2. The value of m in this case is calculated as [6, page 78,118]:

< / BR>
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2. Different random signal that has passed through the device with the amplitude characteristic (11) and having a maximum amplitude A, and the sum of this signal with a non-random signal with amplitude a (this is a typical case detection signal to the background noise). In this case, the value of m1and1are calculated by the formulas (26) and (27), and the values of m2and2formula:

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< / BR>
In both cases, the probability of distinguishing D determined by calculation and experiment for signals with amplitudes are distributed according to the Rayleigh law. Calculations and experiments set: p1= p2= 1 and F = 0,001, the parameter g in the formula (11) is set equal to 0.8, the number of summed values of xnand (x+a)nissued 50000, number of amounts in the experiments - 10000.

In table. 6 and 7 presents the results distinguish between the two the results of the calculation, in the third experiment results.

In table. 7 and in Fig. 8 presents the results distinguish between random signal with a maximum amplitude A = 1 and the sum of this signal with a non-random signal with amplitude a = 0,002. The second line of the table results of the experiment.

From table. 6 and 7 shows that in the case of artificial restrictions amplitudes device having the amplitude response "with saturation", the method according to the invention allows to increase the probability of distinguishing signals.

In particular, table. 6 and Fig. 7 show that the probability of discernment more than the prototype (n=2), obtained when n 50. Similar to the result in table 7 and Fig. 8, but with n 10.

We also note that the invariance of the way to species distribution amplitudes: a high probability of discernment when n >>received 2 days a Rayleigh distribution, rice, gamma distribution, and the distribution of the resulting transformation of the amplitudes by the formula (11).

Summarizing the obtained results, we can conclude: with limited distributions of the amplitudes of the proposed method is the summation of the amplitudes, raised to the power of n>>2 - allows you to get a higher probability of discernment is retene.

In the device (Fig. 1) designed to distinguish between signals generated two parallel channel. The first channel is designed to distinguish between signals with almost unlimited amplitudes, so it uses the procedure of discernment used in the prototype, i.e., the values of the amplitudes are squared, summed and the sum is compared with a threshold. The second channel is designed to distinguish between signals with reduced amplitudes. It the procedure of distinction lies in the construction of values of amplitudes in the degree a lot more than the second, the summation of the results and comparison of the sum with a threshold. The threshold for each channel is calculated separately based on a given probability of exceeding his signal with less power for both channels are set the same. The specific value of the exponent in the second channel is selected based on the expected probability characteristics amplitude.

The result of application of the considered device is as follows: if the amplitude of the analyzed signal are virtually unlimited, with the highest probability of exceeding the threshold signal with more power going to happen in the first channel; if the amplitude of the analyzed signage example, using the results of table 2. Assume that the exponent n in the second channel is set to 1000. Then in distinguishing signals with unlimited amplitudes (k = 1) the probability of exceeding a threshold in the first channel (n = 2) is equal to 0.19, and the second of 0.002, i.e., more likely to be a distinction in the first channel, but the probability is small. In distinguishing signals with reduced amplitudes (for example, k = 1,001) the probability of exceeding a threshold in the first channel is equal to 0.20, the second of 0.96, i.e., more likely to occur discernment in the second channel and the probability value will be large.

Literature:

1. The dulevich C. E., Korostelev, A. A. and other Theoretical bases of radar. "Soviet radio", Moscow, 1964, page 113, 215, 221, 242.

2. Modern radar. Analysis, calculation and design of systems. Translation from English under the editorship of Kobzar Y. B. "Soviet radio", Moscow, 1969. p. 124.

3. Levin, B. R. Theoretical foundations of statistical radio engineering. The second book. "Soviet radio", Moscow, 1968, page 355, 366.

4. Wentzel E. C. probability Theory. Fizmatgiz, Moscow, 1962, page 116, 551.

5. Tikhonov Century. And. Statistical radio engineering. "Soviet radio, Moscow, 1966, pp. 56, 57, 395 the n, 1969 p. 78, 103, 118, 135, 149, 150, 154.

The way to distinguish between random radar signals, consisting in the fact that radar signals reflected from objects locations, serves on the input of the amplitude detector at time t and detects them, the values of the amplitudes of videokursov in one processing channel square, then the sum of the N values of the transformed amplitudes videokursov, and N = t/T where T is the repetition period of videokursov determine Horny value of the sum of the values of the amplitudes of Ya 0.1, and then compare the sum of the converted values of the amplitudes of videokursov Y1with a threshold value of Ya 0.1, characterized in that the detector output signals videokursov branch into two channels, and the branched signals are simultaneously fed to the inputs of the first and second processing channels amplitudes videokursov, in the second processing channel values of the amplitudes of videokursov erected in the degree a lot more than the second, the converted values of the amplitudes in the second channel summarize, determine the threshold value of this sum Yof 0.2, the sum of the values of the transformed amplitudes Y2the second channel is compared with the threshold value of Yof 0.2this same channel, decide what obrazovannyh values of the amplitudes of Y1or Y2will exceed the level of Ya 0.1or Yof 0.2the threshold of her channel.

 

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